ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Yingxiang Xu
S. 182 - 209 doi:10.1553/etna_vol49s182 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol49s182
Abstract: Optimized Schwarz methods enhance convergence using optimized transmission conditions between subdomains. The optimization is usually performed for a model problem on an unbounded domain and two subdomains represented by half spaces. The influence of the domain decomposition geometry on the convergence and the optimized parameters is thus lost in the process, and it is not even theoretically clear if the results published for the unbounded domain still hold in concrete applications where the domains are bounded. We prove here rigorously for a two-subdomain decomposition that the asymptotic performance of optimized Schwarz methods derived from an unbounded domain analysis still holds in the case of a bounded domain, but the constants in the best choice of parameters and convergence rate estimates are influenced by the domain truncation. We obtain accurate estimates for this influence and show theoretically that the domain truncation has more remarkable influence for the slowly converging optimized Schwarz methods than for those converging fast. When the subdomain size is very small, our new optimized parameters lead to much faster algorithms than those obtained from an unbounded domain analysis. We illustrate our theoretical results with numerical experiments. Keywords: optimized Schwarz methods, domain decomposition methods, transmission conditions, influence of domain truncation Published Online: 2018/10/11 11:34:58 Object Identifier: 0xc1aa5572 0x0039f7d2 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |